Two-dimensional quantum measurements through multimode optical parametric amplification : From multimode squeezing to SU(1, 1) interferometer

This thesis presents the experimental realization and investigation of spatial multimode optical parametric amplification (MOPA) using a nonlinear bulk BBO type-I crystal. Firstly, MOPA is used as a novel approach to measure the squeezing of the strongest modes within multimode squeezed radiation. Squeezing refers to the reduction of fluctuations below the classical limit, as determined by the statistical quantum nature of bosonic particles (photons). This limit is known as the shot noise limit (SNL). The key process to achieve this is the strong, lossless amplification of the squeezed/anti-squeezed quadratures of these modes. This differs from the traditional method of measuring squeezing, which typically requires a reference local oscillator, complicated and lossy modal filtering, and repeated measurements for each selected mode. Instead, this novel method enables simultaneous measurement through direct intensity detection using a camera. Practically, this can be achieved using two non-linear crystals, one for generating the squeezed modes (squeezer) and the other pumped with high power for strongly amplifying them (the amplifier), this same arrangement is called SU(1, 1) interferometer. The use of two crystals indicates the necessity of careful experimental design to attain an optimal matching of the squeezed modes with the input amplifier modes. Despite the low number of photons for each squeezed modes and the high susceptibility of squeezing to losses, the conducted measurements successfully measure the squeezing and anti-squeezing for 8 squeezed vacuum modes, with strongest squeezing at −5.2 ± 0.2 dB. Secondly, the phase sensitivity, which refers to the accuracy with which a measurement system can detect and measure the phase of light, is evaluated across the two-dimensional spatially distributed multimode squeezed vacuum and is shown to exceed the typical shot noise limit. This is achieved by measuring the alternating phase caused by the driven movement of a spherical mirror in the SU(1, 1) interferometer. This mirror also plays a pivotal role in imaging the multimode squeezing back into the nonlinear crystal and realigning it with the amplifier modes. The quantum advantage of the phase sensitivity is demonstrated across the two-dimensional spatial area within the intensity distribution of the optical parametric amplifier (OPA). This paves the way for various applications that have previously been performed using only classical methods. As demonstrated in this work, it enables practical measurements such as determining phase maps of an optical surface, the ideal position of a mirror within an interferometer, and all of this can be achieved with a very low flux of sensing photons. To this point, all measurements were conducted using the far-field radiation from the MOPA. Lastly, to circumvent the inherent phase correlation between the generated photons in the far field of the bipartite radiation, the two-dimensional phase sensitivity of the SU(1, 1) interferometer is demonstrated in the near-field imaging/detection scheme. This configuration involves imaging a plane mirror in the near field with a lens before amplification. The achieved phase indistinguishability of photon pairs in the interferometer allows for accurate extraction of the true relative phase values due to the mirror’s surface, with a sensitivity that surpasses the shot noise limit, which is especially beneficial if only a low number of photons for the detection is allowed. This measurement demonstrates the quantum advantage across a two-dimensional spatial area, achieving phase sensitivity that exceeds the shot noise limit (SNL) by 5.1 ± 1.2 dB.